Dark current mechanism of terahertz quantum-well photodetectorsJ. Y. Jia, J. H. Gao, M. R. Hao, T. M. Wang, W. Z. Shen, Y. H. Zhang, J. C. Cao, X. G. Guo, and H. Schneider Citation: Journal of Applied Physics 116, 154501 (2014); doi: 10.1063/1.4898036 View online: http://dx.doi.org/10.1063/1.4898036 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/15?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Terahertz quantum-well photodetectors: Design, performance, and improvements J. Appl. Phys. 114, 194507 (2013); 10.1063/1.4826625 Negative differential resistance induced by thermalization of two-dimensional electrons in terahertz quantum-wellphotodetectors J. Appl. Phys. 113, 203109 (2013); 10.1063/1.4808343 Background-limited terahertz quantum-well photodetector Appl. Phys. Lett. 86, 231103 (2005); 10.1063/1.1947377 Asymmetry in the dark current low frequency noise characteristics of B–B and B–C quantum well infraredphotodetectors from 10 to 80 K J. Appl. Phys. 87, 2400 (2000); 10.1063/1.372192 Noise characteristics of quantum-well infrared photodetectors at low temperatures Appl. Phys. Lett. 76, 206 (2000); 10.1063/1.125703

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Dark current mechanism of terahertz quantum-well photodetectors

J. Y. Jia,1 J. H. Gao,1 M. R. Hao,1 T. M. Wang,1 W. Z. Shen,1 Y. H. Zhang,1,a) J. C. Cao,2

X. G. Guo,2 and H. Schneider3,b)

1Key Laboratory of Artificial Structures and Quantum Control (Ministry of Education), Department of Physicsand Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China2Key Laboratory of Terahertz Solid-State Technology, Shanghai Institute of Microsystem and InformationTechnology, Chinese Academy of Sciences, 865 Changning Road, Shanghai 200050, China3Helmholtz-Zentrum Dresden-Rossendorf, Institute of Ion Beam Physics and Materials Research,P.O. Box 510119, 01314 Dresden, Germany

(Received 15 August 2014; accepted 29 September 2014; published online 15 October 2014)

Dark current mechanisms of terahertz quantum-well photodetectors (THz QWPs) are systematically

investigated experimentally and theoretically by measuring two newly designed structures combined

with samples reported previously. In contrast to previous investigations, scattering-assisted

tunneling dark current is found to cause significant contributions to total dark current. A criterion

is also proposed to determine the major dark current mechanism at different peak response

frequencies. We further determine background limited performance (BLIP) temperatures, which

decrease both experimentally and theoretically as the electric field increases. This work gives good

description of dark current mechanism for QWPs in the THz region and is extended to determine

the transition fields and BLIP temperatures with response peaks from 3 to 12 THz. VC 2014AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4898036]

I. INTRODUCTION

Presently, terahertz quantum-well photodetectors (THz

QWPs) have emerged as one promising candidate to realize

compact, high speed, and high frequency detectors for the

THz region due to the characteristics of intersubband transi-

tions and unipolar transport properties. Compared with other

detectors in THz region, such as Si bolometers, pyroelectric

detectors made from LiTaO3 crystals and heterodyne detec-

tors made from low temperature superconductor films,1,2

THz QWPs have their own advantages. The first and

foremost important advantage relates to the availability of a

mature material and processing technology for QWPs based

on GaAs, which makes it possible to fabricate large-scale

uniform, high resolution, and long-term stable THz QWP

focal plane arrays. Second, they are narrow band and enable

wide wavelength coverage by adjusting the intersubband

transition energy. The other distinct advantage of THz

QWPs is their intrinsic high speed due to the inherent short

carrier lifetime, which helps to create new applications in,

for example, environmental remote sensing of molecules and

long-wavelength laser-based communication.3 THz QWPs

are designed as a natural extension of quantum well infrared

(IR) photodetectors4 and many researchers have been

conducted to achieve better performance5–7 after their first

experimental demonstration.8–10 Dark current, which has

been investigated extensively in mid-infrared QWPs,4 is a

key parameter to determine the performance of QWPs.

Different from mid-IR QWPs, QWPs in THz region have

lower barrier height, lower working temperature, and bias.

Additional physical effects including exchange-correlation

and depolarization, which could be ignored in mid-IR QWPs

must be included. However, only limited investigations have

been carried out on dark current mechanisms of THz QWPs.

Recently, Ferr�e et al. exploited many-body effects to

improve the design of THz QWPs for lower dark current.11

Tan et al. have simulated the dark current of a 3.2 THz QWP

and got the conclusion that the thermionic emission mecha-

nism is the major mechanism to dark current.12 But previous

investigations have only been conducted on the basis of one

specific sample and detailed dark current mechanisms of

THz QWPs have not been elaborated.

In this paper, we systematically investigate the dark cur-

rent mechanism of THz QWPs ranging from 3 to 12 THz

experimentally and theoretically by using newly designed

QWP structures (L924, L925) combined with other samples

(v265, v266, v267) initially proposed by Liu.8 We also pro-

pose the transition fields at different peak frequencies for

THz QWPs as a criterion to determine the dominant dark

current mechanism. Moreover, experimental and theoretical

results on background limited performance (BLIP) tempera-

ture considering different dark current mechanisms are given

and discussed in detail.

II. THEORY AND MODEL

Fig. 1 shows the schematic plot of the physical proc-

esses contributing to dark current of THz QWPs. First,

interwell tunneling, which could be neglected due to the

designed wide barriers, involves electrons scattering from

the ground state in one quantum well (QW) into the next.

Second, thermionic emission (TE) refers to thermal excita-

tion of electrons from the upper part (with energy greater

than the barrier height) of the ground state to the noncon-

fined continuum on the top of the barrier. Finally,

scattering-assisted Fowler-Nordheim tunneling (SAT)

a)Electronic mail: yuehzhang@sjtu.edu.cn.b)Electronic mail: h.schneider@hzdr.de

0021-8979/2014/116(15)/154501/6/$30.00 VC 2014 AIP Publishing LLC116, 154501-1

JOURNAL OF APPLIED PHYSICS 116, 154501 (2014)

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means confined electrons of the ground state slightly below

the barrier height could be scattered by either phonons or

electrons from QWs into the continuum through the tip of

the barriers. Lw and Lb are the QW width and barrier width,

respectively. F is the electric field applied to the THz QWP

samples. Vb is the original barrier height, while

V¼Vb� eFLw/2 is the barrier height lowering by applied

electric field. According to the emission-capture model, we

give the dark current by4

Jdark ¼ev Fð Þsc

sscatt

ð1E1

m

p�h2Lp

T E;Fð Þ 1þ expE� Ef

kBT

� �� ��1

dE:

(1)

The drift velocity is taken of the usual form v(F)¼lF/[1þ (lF/vsat)

2]1/2. Values of l¼ 5000 cm2/Vs for the

excited-electron mobility and vsat ¼ 107 cms�1 for the satu-

rated velocity were used in calculation. sscatt is the scattering

time of electrons from the ground state into the continuum

state and sc is the capture time from the continuum back to

the ground state. For sample L925 with transition energy

�47 meV, the life time of excited electron sc is mainly deter-

mined by optical phonon scattering and electron-electron

scattering, which is expected to have similar value as in mid-

infrared QWPs. However, for L924 whose transition energy

(28 meV) is smaller than the LO phonon energy of GaAs

(36 meV), electron-electron scattering becomes the dominant

mechanism, which is expected to cause a reduced capture

probability and, thus, an increased sc. In this model, sc and

sscatt just enter linearly and not in the exponent (see Eq. (1)

and Eqs. (4) and (5) below). As a result, a small deviation in

the estimation of sc and sscatt will have weak impact on the

results of dark current and BLIP temperature. So, the scatter-

ing time is set as sscatt ¼ 5 ps, the values of life time of

excited electrons are set as sc¼ 8 ps for sample L925 and

sc¼ 10 ps for L924.7 Lp is the period length of the multiple

quantum-well structure and equals the sum of QW and bar-

rier widths. Ef is the temperature dependent Fermi level in

the QWs given by13

Ef Tð Þ ¼ kBTln expp�h2LdopeN3Ddope

m�kBT

!� 1

" #; (2)

where N3Ddope is the 3D doping density in the center of

GaAs QWs and Ldope is the doping length. T(E,F) is the

transmission coefficient calculated using Wentzel-Kramers-

Brillouin (WKB) approximation. For energy higher than the

barrier (for E>V), T(E,F)¼ 1. Equation (1) could be simpli-

fied in pure TE regime and the dark current obtained corre-

sponds to TE dark current as marked in Fig. 1. For energy

less than the barrier height, T(E,F) could be given as4

TðE;FÞ ¼ exp �2

ðzc

0

dzffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2mbðV � E� eFzÞ

p=�h

� �; (3)

where mb is the barrier mass, zc¼ (V�E)/eF is defined

as the classical tunneling point. As shown in Fig. 1, when

V� eFLb < E < V, the dark current obtained corresponds to

SAT dark current. When E1 < E < V�eFLb, the dark current

obtained corresponds to interwell tunneling dark current,

which is far less than TE and SAT dark current in operation

temperatures and biases.

III. EXPERIMENT AND DISCUSSION

A. Devices, fabrication, and measuring

We have designed two THz QWP structures, which

were grown on semi-insulating GaAs wafers by molecular

beam epitaxy. Both samples (samples L924 and L925)

consist of a number of GaAs/AlGaAs QWs sandwiched

between 400 nm and 800 nm thick n-type contact layers on

the top and bottom sides, respectively, with doping density

of 1017 cm�3 in the contact layers. Detailed design parame-

ters are listed in Table I. The well width, Al fraction, and

doping density are optimally designed such that only one

energy state E1 is bound in the QW and the excited state E2

is close to resonance with the bottom of the barrier conduc-

tion band. Also, many-body effects including: Hartree

potential energy, exchange-correlation potential energy, and

depolarization energy have been taken into consideration in

the design.7,14–16 The barrier width was chosen nearly five

times of the well width to suppress the interwell tunneling

dark current. Mesa devices with different sizes were fabri-

cated using standard GaAs processing techniques with

metal top contacts. For optical characterization, samples

were polished to give rise to a 45� facet and packaged into

the standard double-pass back side illumination geometry

FIG. 1. Schematic plot of physical regimes contributing to the dark current

of THz QWPs. Interwell tunneling dark current is neglected due to our

designed wide barriers.

TABLE I. Structure parameters of THz QWPs. Lw is the well width, Lb is

the barrier width, Alx is the barrier aluminum fraction, N3Ddope is 3D doping

concentration in the center of the well. Ldope is the doping region width. N is

the number of QWs, �p is the measured response peak. The GaAs/AlGaAs

MQWs are sandwiched between 400 nm top and 800 nm bottom GaAs

contact layer doped with Si to 1017 cm�3.

Sample

Lw

(nm)

Lb

(nm) Alx (%)

N3Ddope

(cm�3)

Ldope

(nm) N�p

(THz)

L924 12 64 4 1� 1017 7 35 6.78

L925 9.6 50 7 1� 1017 9.6 40 � 11.37

154501-2 Jia et al. J. Appl. Phys. 116, 154501 (2014)

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with an internal incident angle of 45�. All samples’ charac-

teristics were performed in a helium cryostat and the photo-

current spectra were measured with a Fourier transform

infrared spectrometer (Bruker IFS 66 S/V) with glowbar

source and a Mylar 6u beam splitter.

B. Dark current mechanisms

Figs. 2(a) and 2(b) show the calculated and measured

dark current of samples L924 and L925 at various tempera-

tures. As shown, the calculated dark currents (solid lines),

which equal the sum of TE dark current (dotted lines) and

SAT dark current (dashed lines), agree well with the experi-

mental measurements (bullets) at different bias voltages and

temperatures for both samples. The deviation in the low

temperature region (14 K for L924 and 22.5 K for L925) sug-

gests that the measured dark current decreases more slowly

than expected below 16 K for L924 and 25 K for L925. This

behavior is likely caused by tunneling such as direct inter-

well and hopping-like via deep-impurity levels in the barrier.

The tunneling is much less than TE and SAT at higher tem-

peratures, but makes non-negligible contribution to the dark

current in the low temperature region. For sample L924 in

Fig. 2(a), SAT dark current is an important part of the dark

current at its normal working bias voltages as well as TE

dark current. The transition field, defined as the electric field

at which SAT dark current equals TE dark current, show an

upward trend as 459, 538, 650, 744, 994, and 1298 V/cm

with the temperatures of 14, 16, 18, 20, 25, and 30 K, respec-

tively. The reason is that TE dark current increases more

quickly than SAT dark current as the temperatures rise, such

that bigger transition fields are reached.

In addition, it is interesting to note that the measured

dark current becomes larger than the calculated one, when

the sample is biased near the breakdown field of 2203 V/cm

(0.6 V bias). This breakdown occurs since the extra elec-

trons, which are usually confined in QW can leak across the

barriers due to an efficient ionization of the first QW, as has

been discussed in more detail by Gomez et al.,17 Delga

et al.,18 and Guo et al.19 However, when it comes to high

temperature, most of the confined electrons escape into the

continuum already by TE and SAT and the relative contribu-

tion by extra leakage due to ionization becomes negligible.

For sample L925 shown in Fig. 2(b), the measurement and

theoretical calculations are carried out up to 4100 V/cm (1 V

bias) and temperatures from 22.5 to 32.5 K. The transition

fields are 848, 993, 1143, 1277, and 1440 V/cm for tempera-

tures of 22.5, 25, 27.5, 30, and 32.5 V, which are far below

the breakdown field of 4108 V/cm. Moreover, the dark cur-

rent simulations are also performed for the samples reported

in Ref. 8. For sample v267 with peak response frequency of

3.2 THz, we reach the same conclusion as Tan,12 i.e. that the

TE contribution is dominant in dark current. The main rea-

son is that the maximum breakdown field (107 V/cm) that

could be applied at the operation temperature is much

smaller than the transition fields, such that the SAT regime

could never be reached for this sample. For sample v266

with response peak position of 5.4 THz, both TE dark current

and SAT dark current are significant parts in its working

electric fields and temperatures.

To provide a fundamental criterion to determine which

mechanism is dominant in total dark current for THz QWPs

with different peak response frequencies, we give the calcu-

lated transition fields in Fig. 3. The temperatures used are the

BLIP temperatures when TE dark current dominates and the

structure parameters used are optimally designed in Ref. 7.

As shown, if the THz QWP device is operated at a bias

below the transition field, TE process is the major contribu-

tion for the dark current. Otherwise, the SAT dark current is

dominant. Measured breakdown fields and calculated transi-

tion fields for samples v265, v266, v267, L924, and L925 are

also presented in Fig. 3. The little difference in structure

FIG. 2. Experimental (bullets) and calculated (dotted, dashed, and solid

lines) dark current of samples (a) L924 and (b) L925 at various tempera-

tures. The dashed and dotted lines represent TE dark current and SAT dark

current, respectively. The solid lines are the total dark current.

FIG. 3. Calculated transition fields for THz QWPs with different response

peak frequencies. Structure parameters used are designed in Ref. 7.

Temperatures used are the BLIP temperatures when TE dark current is the

dominant. Measured breakdown fields (solid squares) and calculated transi-

tion fields (solid circles) are also presented for samples v265, v266, v267,

L924, and L925.

154501-3 Jia et al. J. Appl. Phys. 116, 154501 (2014)

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parameters of experimental samples and designed ones may

account for the small deviation in the transition fields.

Except v267, whose dark current mechanism is always TE

dominant due to its breakdown field less than transition field,

SAT dark current could be the major mechanism for all other

samples in normal operation bias. From the breakdown fields

and transition fields shown, we can conclude that TE is the

major dark current mechanism for THz QWPs with very low

peak response frequencies (below about 4 THz) in their

working biases, while SAT dark current can be much larger

than TE for higher frequency THz QWPs in their normal

operation biases. As a summary, the SAT process is a very

significant dark current regime for THz QWPs since higher

bias leads to increased responsivity, which helps to realize

the stable operation of THz QWP devices by reducing the

influence of unwanted noise sources (e.g., amplifier noise).

C. BLIP temperature

On the basis of the above systematical investigation on

dark current mechanisms of THz QWPs, we further intro-

duce the BLIP temperature taken as the temperature at

which background photocurrent equals the dark current,

which is a significant parameter reflecting the performance

of QWPs. BLIP temperatures were measured by comparing

current-voltage (I-V) curves under dark condition (Id) and

under a 300 K background (Ibg) with 90� field of view

(FOV) at different temperatures. Measured I-V curves are

shown in Figs. 4(a) and 4(b) for samples L924 and L925,

respectively. As is shown in Fig. 4(a) for L924, when the

bias is increased to a threshold value of 0.6 V, the currents

show an abrupt increase of more than one order of magni-

tude, which is due to barrier breakdown caused by ioniza-

tion of the first QW.17 For L925 in Fig. 4(b), when

temperature dropped below 20 K, the dark currents stop

decreasing and remain constant. This behavior is partly due

to the remaining tunneling. The tunneling dark current is so

low as compared to the background photocurrent that it

could be ignored when the device works in BLIP regime. To

theoretically investigate the BLIP temperatures, we first

give the photocurrent by

Jphoton ¼ e/B;phggphoto; (4)

where /B;ph is incident photon flux number given by

/B;ph ¼Ð

d�ðp sin2 h2Þgð�ÞLBð�Þ. LBð�Þ is the photon irradi-

ance, which can be written as LBð�Þ ¼ 2�2

c21

eh�=kBTB�1, TB is

background temperature. The spectral lineshape gð�Þ ¼C2

ðh��h�pÞ2þC2 with the peak response frequency �p, the cut-off

response frequency �c ¼ 1:1� �p, and the Lorentzian line-

width constant C ¼ h�c � h�p matches well with the shapes

of measured photocurrent spectra for both samples shown in

Fig. 3(c). The main dark region from 256 to 292 cm�1 in

sample L924 is due to GaAs optical phonon absorption in

the substrate, other small features such as the dips at 312 and

338 cm�1 are caused by two-phonon absorption. The dip at

362 cm�1 in both samples corresponds to the AlAs-like

phonon absorption.

The quite broad photoresponse spectra for both samples

indicate that the intersubband transitions are of bound-to-

continuum type. For this bound-to-continuum case, the

escape process of excited electrons takes little time, i.e.,

once an electron is excited, it is already in the continuum. In

this case, an escape probability equal to one is a good

approximation for practical proposes and as a result, the

photoconductive gain is taken as gphoto � scv=NLp. The

absorption efficiency is given by g ¼ e2h4e0nrm�wc

sin2hcos h N3Ddopef

1p

Cðht�E21Þ2þC2, h ¼ 45� is the angle between THz radiation

propagating direction and QW’s growth direction, and

f ¼ 4pm�wt�h jhu2jzju1ij2 is the oscillator strength. From Eqs. (1)

to (4), the BLIP temperature is determined by the following

equation:

/B;phg1ð Þsscatt ¼

m

p�h2

ð1E1

T E;Fð Þ 1þ expE� Ef

kBT

� �� ��1

dE;

(5)

where gð1Þ is the absorption efficiency per QW.

In Fig. 5(a), measured BLIP temperatures under differ-

ent electric fields are shown (symbols) for samples v265,

v266, L924, and L925. Calculated BLIP temperatures versus

bias voltages are also presented with solid lines, which agree

FIG. 4. Current-voltage curves under dark condition (solid lines) and under

90� FOV 300 K background (dashed lines) for samples (a) L924 and (b)

L925 at various temperatures. (c) Measured photocurrent spectra (solid

lines) and fitted ones (dashed lines) for samples L924 and L925.

154501-4 Jia et al. J. Appl. Phys. 116, 154501 (2014)

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202.120.52.96 On: Mon, 24 Nov 2014 01:15:16

reasonably well with the experimental data. As shown, an

obvious decrease of BLIP temperatures with increasing elec-

tric field is found due to the sharp increase of SAT dark cur-

rent. For samples L925 and v265, measured BLIP

temperatures are lower than the calculated ones. This may

partly be caused by the decrease of the photon flux by pho-

non absorption, which could be seen from the photocurrent

spectra in Fig. 4(c). In addition, it is hard to determine the

real intersubband transition frequencies of these two samples

due to the phonon absorptions, which will also be responsi-

ble for the deviation of the calculated BLIP temperature. In

particular, it should be noted that for a THz QWP working

under a certain bias in BLIP regime, it is usually not appro-

priate to increase the applied electric field for larger output

signals since the signal to noise ratio of the detector will be

sacrificed due to the dramatically rising SAT dark current.

However, if larger signal is preferred and the increase of the

bias is inevitable, the operation temperature of the device

should be lowered to reduce the dark current for reaching

new BLIP regime.

Fig. 5(b) illustrates the calculated BLIP temperature for

THz QWPs with different peak detection frequencies consid-

ering the effect of applied electric field on the dark current.

As shown, when the sample is operated at small bias, i.e., TE

is the dominant dark current, the calculated BLIP tempera-

ture obtained is consistent with calculated and experimental

results reported before.8,9 When the applied electric field

increases towards the transition field such that TE dark cur-

rent equals the SAT dark current, the BLIP temperatures

obtained are slightly lower than BLIP temperatures when TE

dominates. When the electric field approaches the break-

down field, SAT is always the major dark current process for

QWP samples with higher peak response frequencies in the

THz region, which will further decrease the BLIP tempera-

ture. Experimental measured BLIP temperatures for samples

v266, L924, v265, and L925 are presented and show a

decrease trend with bias increasing. In particular, the BLIP

temperatures for sample L924 (6.78 THz peak frequency)

and L925 (11.37 THz) are about 20% lower at high bias

close to the breakdown field(2203 and 4108 V/cm, respec-

tively) than at low bias.

IV. CONCLUSION

In conclusion, we have investigated the dark current

mechanism of THz QWPs experimentally and theoretically

using two newly designed THz QWPs in combination with

existing samples. By comparison of the calculated dark

current with experiments, we illustrate that the SAT dark

current is a significant part of the total dark current as well as

the TE dark current under normal working bias. In the opera-

tion of THz QWPs, high working bias is always preferred for

increased responsivity, such that SAT dark current will occur

and should be taken into account in analysis of THz QWPs’

performance. We also proposed the transition fields for THz

QWPs with different response peaks as a criterion to deter-

mine the main mechanism of dark current. Moreover, con-

sidering the sharp increase of SAT dark current with bias

voltage, calculated BLIP temperatures show a downward

trend, which was confirmed by the experiments. For further

description, we give the BLIP temperatures for THz QWPs

with different peak response frequencies accounting for the

contribution of SAT dark current. Our theoretical and experi-

mental results show that SAT, which is well known for

mid-infrared QWPs but has been ignored in previous investi-

gations for QWPs in THz region,5,7,12,14,16–18 should be

noted to play a key role in total dark current, and its further

effect on the performance such as BLIP temperature has to

be taken into consideration.

ACKNOWLEDGMENTS

The authors were deeply indebted to Professor H. C. Liu

for his huge contribution to this work, until his sudden death

in October 2013. The authors also thank E. H. Linfield and

L. H. Li for the growths of wafers. This work was supported

in part by 863 Program of China (2011AA010205), the

Natural Science Foundation of China (91221201, 61234005,

and 11074167), and the National Major Basic Research

Projects (2011CB925603).

1M. Hajenius, J. J. A. Baselmans, A. Baryshev, J. R. Gao, T. M. Klapwijk,

J. W. Kooi, W. Jellema, and Z. Q. Yang, J. Appl. Phys. 100, 074507

(2006).

FIG. 5. (a) Measured (symbols) and calculated (solid lines) BLIP tempera-

tures at different fields for samples v266, L924, v265, and L925. In the cal-

culation, the maximum indicated electric fields are the respective

breakdown fields. (b) Measured (symbols) BLIP temperatures for samples

v266, L924, v265, and L925 at different biases and calculated BLIP temper-

atures for different peak response frequencies, when sample is operated at a

small bias such that TE is the dominant dark current (solid line) and a bias at

which TE equals SAT(dashed line). Vertical arrows indicate the field-

induced decrease of the BLIP temperature.

154501-5 Jia et al. J. Appl. Phys. 116, 154501 (2014)

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202.120.52.96 On: Mon, 24 Nov 2014 01:15:16

2P. Khosropanah, W. Zhang, J. N. Hovenier, J. R. Gao, T. M. Klapwijk, M.

I. Amanti, G. Scalari, and J. Faist, J. Appl. Phys. 104, 113106 (2008).3X. G. Guo, J. C. Cao, R. Zhang, Z. Y. Tan, and H. C. Liu, IEEE J. Sel.

Top. Quantum Electron. 19, 8500508 (2013).4H. Schneider and H. C. Liu, Quantum Well Infrared Photodetectors:Physics and Applications (Springer, 2007).

5H. C. Liu, H. Luo, C. Y. Song, Z. R. Wasilewski, A. J. S. Thorpe, and J. C.

Cao, Infrared Phys. Technol. 50, 191 (2007).6H. Schneider, H. C. Liu, S. Winnerl, C. Y. Song, M. Walther, and M.

Helm, Opt. Express 17, 12279 (2009).7S. Zhang, T. M. Wang, M. R. Hao, Y. Yang, Y. H. Zhang, W. Z. Shen,

and H. C. Liu, J. Appl. Phys. 114, 194507 (2013).8H. Luo, H. C. Liu, C. Y. Song, and Z. R. Wasilewski, Appl. Phys. Lett. 86,

231103 (2005).9H. C. Liu, C. Y. Song, A. J. S. Thorpe, and J. C. Cao, Appl. Phys. Lett. 84,

4068 (2004).10M. Graf, G. Scalari, D. Hofstetter, J. Faist, H. Beere, E. Linfield, D.

Ritchie, and G. Davies, Appl. Phys. Lett. 84, 475 (2004).

11S. Ferr�e, S. G. Razavipour, and D. Ban, Appl. Phys. Lett. 103, 081105

(2013).12Z. Y. Tan, X. G. Guo, J. C. Cao, H. Li, X. Wang, S. L. Feng, Z. R.

Wasilewski, and H. C. Liu, Semicond. Sci. Technol. 24, 115014 (2009).13B. F. Levine, J. Appl. Phys. 74, R1 (1993).14M. Graf, E. Dupont, H. Luo, S. Haffouz, Z. R. Wasilewski, A. J. S.

Thorpe, D. Ban, and H. C. Liu, Infrared Phys. Technol. 52, 289 (2009).15X. G. Guo, Z. Y. Tan, J. C. Cao, and H. C. Liu, Appl. Phys. Lett. 94,

201101 (2009).16X. G. Guo, R. Zhang, H. C. Liu, A. J. S. Thorpe, and J. C. Cao, Appl.

Phys. Lett. 97, 021114 (2010).17A. Gomez, V. Berger, N. Pere-Laperne, and L.-A. de Vaulchier, Appl.

Phys. Lett. 92, 202110 (2008).18A. Delga, L. Doyennette, A. Buffaz, V. Berger, F. R. Jasnot, L. A. de

Vaulchier, N. P�er�e-Laperne, and H. C. Liu, J. Appl. Phys. 110, 013714

(2011).19X. G. Guo, L. L. Gu, M. Dong, J. C. Cao, H. C. Liu, and F. M. Guo,

J. Appl. Phys. 113, 203109 (2013).

154501-6 Jia et al. J. Appl. Phys. 116, 154501 (2014)

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